Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest numbers you've ever seen in your life.
Notation for progressively larger numbers.
5 tetrated can be written as 5 to the power of 5^5^5^5 mod 10, mod 11
Consider the number 4. To make a larger number out of 4, you might add 4 to 4 and get 8. You might multiply by 4 to get 16. Or you might raise 4 to the power of itself: 4^4, or 256. But what if you took that a step further: Raise 4 to the power of 4, 4 times:
That's 4 tetrated, or . That's a very, very, very big number:
And that's just FOUR tetrated.
Imagine 10 tetrated. 20, 30, 40 tetrated. 100 tetrated. A googol tetrated.
Time for a puzzle.
What is the remainder when you divide
See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html
Tetration and Knuth's Up Notation: TetrationFlags · Template:ConstantsFlag · ConstantTemplate · e